Problem: Simplify the following expression: $\sqrt{20}+\sqrt{125}+\sqrt{45}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{20}+\sqrt{125}+\sqrt{45}$ $= \sqrt{4 \cdot 5}+\sqrt{25 \cdot 5}+\sqrt{9 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{5}+\sqrt{25} \cdot \sqrt{5}+\sqrt{9} \cdot \sqrt{5}$ $= 2\sqrt{5}+5\sqrt{5}+3\sqrt{5}$ Finally, simplify by combining the terms. $= ( 2 + 5 + 3 )\sqrt{5} = 10\sqrt{5}$